About the Two Phase Simplex Method
The two phase simplex method solves linear programming models that need artificial variables. It is useful when constraints include greater than or equal signs, equalities, or awkward starting points. Phase I searches for a feasible basic solution. Phase II uses that feasible basis to improve the real objective.
Why This Calculator Helps
Manual tableau work can become slow. Each pivot must be selected with care. A single ratio error may change the answer. This calculator builds the standard form, adds slack variables, adds surplus variables, and adds artificial variables where needed. It then runs Phase I and Phase II with clear rows, reduced costs, and final variable values.
Practical Use Cases
Students can check homework steps. Teachers can prepare worked examples. Analysts can test small production, blending, diet, transport, and scheduling models. The calculator assumes nonnegative decision variables. It also expects every constraint to be written with coefficients in the same variable order.
Reading the Output
The report shows whether the model is feasible, optimal, infeasible, or unbounded. Phase I should end with an artificial objective value of zero. If it does not, the original model has no feasible region. In Phase II, positive reduced costs show possible improvement for maximization. The ratio test chooses the leaving row.
Good Modeling Tips
Enter clean coefficients. Use commas between values. Place one constraint on each line. Check that the right hand side is correct. Negative right hand sides are normalized before the algorithm starts. This makes the initial tableau easier to read.
Accuracy Notes
The calculator uses decimal arithmetic and a small tolerance. Very large coefficients or nearly parallel constraints can produce roundoff effects. For sensitive industrial models, confirm the final plan with professional optimization software. Still, this page is a practical learning tool for many classroom and planning problems.
Exporting Results
Use the CSV button for spreadsheet review. Use the PDF button to print or save the visible report. Keep the exported file with your assumptions, because linear programming answers depend strongly on the model you entered. Scenario testing is also useful. Change one resource limit, cost, or profit at a time. Then compare the objective value and active constraints carefully before making final decisions.